Silicon-based mid infrared on-chip gas sensor using Fano resonance of coupled plasmonic microcavities

Sensing in the mid infrared spectral range is highly desirable for the detection and monitoring of different gases. We hereby propose a CMOS compatible silicon-based sensor that operates at (3.5–10 μm) within the mid infrared range. The silicon material is doped to the level that shifts its plasmonic resonance to 3 μm wavelength. The sensor device comprises an in-line rectangular microcavity and a stub microcavity resonator. The resonance frequencies/wavelengths of the two resonators were studied with different design dimensions. When the two resonators are designed to resonate at close frequencies, the interesting Fano resonance with its distinct and sharp line shape is excited due to the interference between the two resonance profiles. Fano resonance is useful for highly sensitive measurements due to its abrupt intensity changing profile. The sensor is studied and analyzed using Finite Difference Element and 2D Finite Difference Time Domain methods. The sensor's performance is characterized by its high sensitivity of 6000 nm/RIU, FOM of 353, and limited insertion loss of 0.45 dB around 6.5 μm operation wavelength. Furthermore, we develop the sensor for simultaneously detecting formaldehyde CH2O and nitrous oxide N2O gases from their strong absorption bands at 3.6 μm and 4.46 μm wavelengths, respectively.

The Fano resonance has been demonstrated in various integrated photonic structures, including waveguides, cavities, and resonators. These structures can be designed to have specific resonant frequencies, and the Fano resonance effect can be used to enhance or suppress the transmission of light at these frequencies. This has led to a wide range of potential applications, such as optical filters, sensors, and modulators, and it is an active area of research in the field of integrated photonics.
Fano resonance is promising in sensing applications since it possesses a distinct sharp line-shape. The excitation of Fano resonance is described by the interference of wide and narrow spectral lines or resonances 17 , which results in a redistribution of the electromagnetic fields in the microcavities.
Different materials and designs were investigated to develop state of the art Fano resonance-based sensors operating in the mid infrared range including graphene and Au nano-antenna arrays 18 , and nanodisks 19 , 1D photonic crystal structure composed of Al, Au, Ag, and Pt 20 , Ag nanorods 21 , Si Lucky knot structure 22 , and the performance of these sensors is compared to our Fano resonance based sensor in Table 1.
In this work, we introduce a Fano resonance based mid infrared sensor which achieves 6000 nm/RIU sensitivity at the 6.5 μm wavelength, and an insertion loss of 0.45 dB. We begin our investigation by analyzing the response of an in-line rectangular cavity resonator 23 and its resonance profiles. Then we study the spectral response and the resonance orders of the stub cavity resonator. Then, we integrate the in-line and stub rectangular cavity resonators in the same device and optimize them to resonate at close frequencies and study the response of these coupled resonators. Finally, we develop the sensor for the detection of two gases on the same chip by exciting two Fano resonances that correspond to the CH 2 O and N 2 O gases strong absorption bands in the mid infrared at 3.6 μm and 4.46 μm 24,25 . Device structure Doped silicon model. To experience plasmonic effects in the mid infrared range, we use Si doped with phosphorus. The n-doped Si model is based on Drude model for metals, where the complex permittivity is evaluated from: where ω p is the plasma frequency in rad/s, ε ∞ is the permittivity at very high frequencies, ω is the frequency in rad/s, and Γ is the collision frequency in rad/s: where m* is the electron effective mass, µ is the carrier mobility and q is the electron charge. The plasma frequency is given by: where N d is the free carrier concentration, and ε 0 is the free-space permittivity. The plasmonic resonance of the doped Si is tuned to the mid infrared above 3 μm for a high doping concentration of 5 × 10 20 cm -3 , while the values of the Drude model parameters were chosen as ε ∞ =11.7, ω p = 2.47 × 10 15 rad/s, and Γ = 9.4 × 10 9 rad/s 6 .

Metal-insulator-metal bus waveguide.
A doped Si wafer of thickness 220 nm on a 3 μm thick sapphire substrate is etched to form the bus waveguide of width 100 nm as shown in Fig. 1. The Si layer is doped by phosphorus with a doping concentration of 5 × 10 20 cm -3 such that its plasma resonant wavelength reaches 3 μm 6 , thereby enabling plasmonic properties at wavelengths in the mid infrared spectral range. A commercial waveguide simulator based on the Finite Difference Eigenmode "FDE" solver 26 was used to calculate the modal properties of the metal-insulator-metal bus waveguide. The FDE solver window was made large enough to enable the electric field intensity to decay to −10 on the log scale, i.e., at the simulation window boundaries ( log E 2 x + E 2 y + E 2 z = −10 ), as shown in Fig. 2a. This was achieved for a length × width equal to 5 μm × 5 μm. At an excitation wavelength of 5 μm, metallic boundary conditions, and mesh steps of 10 nm in both x and y axes, the plasmonic slot waveguide is characterized by a complex effective index of 2.34 + j 3 × 10 -5 , and a modal loss of 3.34 dB/cm. www.nature.com/scientificreports/ The electric field component |Ex| of the excited plasmonic mode is shown in Fig. 2b, the electric field shows strong is confinement in the plasmonic slot with a little power dissipation to the sapphire substrate and to the gas upwards. Moreover, we study the dispersion and the propagation loss of the excited plasmonic mode in the mid infrared range of 4-10 μm as shown in Fig. 3a and b, respectively.   www.nature.com/scientificreports/ In-line rectangular cavity resonator. The FDTD calculations were performed using an electromagnetic simulator 27 to calculate the response and analyze the performance of the proposed designs. A simulation time of 20,000 fs was sufficient to allow all fields including the cavity resonant fields to drop to zero by the end of the simulation process. An auto non-uniform mesh type was implemented which has the highest possible accuracy setting with a minimum mesh step of 0.25 nm. To minimize fields reflections back to the simulation region, 64 uniaxial anisotropic perfectly matched layers were used for the boundary conditions. The response of the in-line rectangular cavity resonator has the form of a bandpass filter 23 as shown in Fig. 4, with the spectral band becomes wider for smaller rectangular widths due to the larger interaction of the fields with the metal boundaries. The Quality-factor defined by (Q = λ/Δλ) where λ is the central wavelength, and Δλ is the FWHM of the resonance band, is shown in Fig. 5, where the Q-factor shows a linear relation with the in-line rectangular resonator width. The length of the rectangular resonator controls the central position of the resonance band as shown in Fig. 6.
The electric field distribution within the rectangular cavity is studied at two different resonant orders as shown in Fig. 7, where strong confinement of the electric field component Ex in the rectangular cavity is observed.
Stub rectangular cavity resonator. The stub rectangular cavity also shows distinct resonance orders but of much sharper lines as shown in Fig. 8, and higher Q-factors. The Q-factor of the 200 nm wide stub waveguide resonance line reaches 350, while that of the in-line resonator of the same width was only 3. Figure 9 shows the electric field component Ex distribution within the stub resonator for two different resonance orders. The stub resonator is characterized by its sharp resonances, where its wavelength positions are given by: where l s is the stub length, n eff is the plasmonic slot mode effective index, and m is the resonance order.   www.nature.com/scientificreports/    www.nature.com/scientificreports/

Fano resonance excitation
The Fano resonance is the result of coupling a discrete localized state to a continuum of states, for example when two oscillators with strongly different damping rates with broad and narrow spectral lines are coupled together 17 .
To excite the Fano resonance in our structure, we integrate the in-line and stub resonators on the same structure and optimize them "based on our studies in the previous sections" to resonate at close frequencies, such that the sharp resonance of the stub resonator couples with the decaying tail of the broader resonance of the in-line resonator as shown in Fig. 10, which shows the excitation of the Fano resonance at 5.5 μm and 6.5 μm wavelengths with an insertion loss of 0.45 dB. Figure 11 shows the electric field distribution in the resonators when the Fano resonance is excited, where it can be observed that at λ = 6 μm, at the top of the broader line, the field is stronger and confined in the in-line cavity. While at the Fano resonance position λ = 6.5 μm, the field is mainly confined in the stub resonator, while the in-line cavity possesses weaker field that corresponds to the decaying tail.
The integrated and coupled resonators structure can be used in sensing applications utilizing the sharpness and high sensitivity of the Fano resonance. The performance and spectral response of the sensor are studied at the 6.5 μm wavelength by varying the surrounding medium refractive index as shown in Fig. 12. The spectral sensitivity "S" defined by the resonant wavelength shift "Δλ" in response to changes in the surrounding gas refractive index "Δn" measured in refractive index unit "RIU", i.e., (S = Δλ/Δn). Moreover, we define the Figure  A comparison between our proposed sensor and recently published Fano sensors in the mid infrared range is demonstrated in Table 1, which shows that our sensor possesses a high sensitivity with a fairly simple design while being CMOS compatible as doped Si and not metals was used for plasmonic effects excitation.  www.nature.com/scientificreports/ Simultaneous-gas sensing in the mid infrared spectral range. Many gases have their strong absorption bands "fingerprints" in the mid infrared. So, for sensing such gases, we excite the highly sensitive Fano resonance within the absorption bands of the target gases. Simultaneous sensing of different gases is achieved by developing the sensor design to include two stub microcavities in addition to the in-line resonator. The waveguide and resonators are covered by a layer of Polydimethylsiloxane (PDMS) with a gas inlet and outlet channels. At the input of the sensor; a Multiplexer (MUX) combines different wavelength signals (λ 1 and λ 2 ) of two laser diodes (LD), similarly, a Demultiplexer (DMUX) distributes the output signals of the sensor to the photodiodes (PD) as shown in Fig. 13. As we have discussed previously, the in-line resonator provides the broad spectrum that will be perturbed at two different wavelength positions resulting in the Fano resonance. Here, we target the detection of two gases of special importance. Firstly, the colorless, flammable Formaldehyde gas CH 2 O which is found in building materials, medical preservatives, fertilizers, and pesticides 28 . Where high levels of exposure to CH 2 O gas could cause some types of cancer 29 . Secondly, the odorless, colorless Nitrous Oxide N 2 O gas supports combustion and its inhalation causes euphoria and body relaxation 30 . So, the monitoring and detection of these two gases in environments where they are produced is of great importance. CH 2 O and N 2 O are detected through their absorption bands at 3.6 μm and 4.46 μm, respectively 24,25 shown in Fig. 14. The transmission spectrum of the multi-gas sensor is shown in Fig. 15, with optimized dimensions of the new structure as w s1 = 0.2 μm, l s1 = 0.85 μm, w s2 = 0.2 μm, l s2 = 1.3 μm, and w i = 0.4 μm, l i = 2.9 μm. The sensitivity and FOM were calculated at both wavelengths of 3.6 μm, and 4.46 μm. At the resonance wavelength of 3.6 μm, a sensitivity of 2300 nm/RIU, and a FOM of 60 were achieved. While at the resonance wavelength of 4.46 μm, the sensitivity reached 3860 nm/ RIU with a calculated FOM of 145.

Fabrication tolerance
Different etching methods are typically used for etching Si wafers after photolithography or electron beam lithography 31 , such as reactive ion etching 32,33 , and inductively coupled plasma dry etching 34 . Hereby, due to its high resolution, we recommend using e-beam lithography to define the metal-insulator-metal waveguide, the rectangular resonator, and the stub resonator. The stub microcavity is obviously less fabrication tolerant than the larger rectangular cavity, so we study the fabrication tolerance of the stub microcavity of dimensions s = 0.2 μm, Figure 11. Electric field |Ex| distribution within the in-line and stub resonators at the Fano resonance wavelength at (a) λ = 6 μm, and (b) λ = 6.5 μm.   www.nature.com/scientificreports/ w s = 0.2 μm, and l i = 0.8 μm in Fig. 16, where its dimensions were changed by ± 10 nm till a fabrication tolerance of 50 nm is reached. While studying the resonators response with the changes in the stub width, it was noticed that the Fano resonance is no longer recognizable for larger widths due to the domination of the wide resonance line of the rectangular cavity, so we limit Fig. 16b to widths with −50 nm fabrication errors. Since the Fano resonance results from the coupling of the sharp stub resonance with the tail of the wider resonance of the in-line resonator, we can define the acceptable fabrication tolerance region of the stub resonator as that wavelength range of the wider resonance tail that would still results in a Fano resonance as a result of coupling with the sharper stub resonance. Qualitatively, this can be defined from the Full Width at a Given Fraction of the Maximum (FWGF). In our case, we choose the fabrication tolerance range to be between FWGF5% and FWGF30%, i.e., Full width at 5% and 30% of the maximum, respectively. This corresponds to a range of acceptable fabrication tolerance of 220 nm for the short wavelength side of the spectrum and 720 nm for the long wavelength side of the spectrum as shown in Fig. 17.

Conclusion
A mid infrared gas sensor was demonstrated and studied. The sensor is composed of a doped Si layer that was etched to form a plasmonic slot waveguide, in-line, and stub cavity resonators. The doping level used pushes the plasmonic resonance of the Si to 3 μm, which results in exhibiting plasmonic properties in the mid infrared range. The performance of each resonator type was investigated individually and then they were both integrated together. When coupled at close frequencies, Fano resonance was excited because of the interference between the wide response of the in-line microcavity and the sharper resonance of the stub resonator. Performance parameters were measured such as the sensitivity, FOM and insertion loss of the device.